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LOCAL PARTITIONED QUANTILE REGRESSION

Published online by Cambridge University Press:  19 September 2016

Zhengyu Zhang
Zhengyu Zhang*
Affiliation:
Shanghai University of Finance and Economics
*
*Address correspondence to Zhengyu Zhang, School of Economics, Shanghai University of Finance and Economics, 777 Guoding Road, 200433 Shanghai, China; e-mail: [email protected].
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Abstract

In this paper, we consider the nonparametric estimation of a broad class of quantile regression models, in which the partially linear, additive, and varying coefficient models are nested. We propose for the model a two-stage kernel-weighted least squares estimator by generalizing the idea of local partitioned mean regression (Christopeit and Hoderlein, 2006, Econometrica 74, 787–817) to a quantile regression framework. The proposed estimator is shown to have desirable asymptotic properties under standard regularity conditions. The new estimator has three advantages relative to existing methods. First, it is structurally simple and widely applicable to the general model as well as its submodels. Second, both the functional coefficients and their derivatives up to any given order can be estimated. Third, the procedure readily extends to censored data, including fixed or random censoring. A Monte Carlo experiment indicates that the proposed estimator performs well in finite samples. An empirical application is also provided.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 5 , October 2017 , pp. 1081 - 1120
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

The author is grateful to the editor Peter C. B. Phillips, a co-editor and two anonymous referees for their constructive comments. Zhengyu Zhang is also affiliated with the Key Laboratory of Mathematical Economics (SUFE), Ministry of Education. The research is supported by the National Science Foundation of China (Grant No. 71501116). Zhengyu Zhang thanks Miffy Lee for her assistance in the research for this article.

References

REFERENCES

Bang, H. & Tsiatis, A.A. (2002) Median regression with censored cost data. Biometrics 58, 643–649.Google ScholarPubMed
Buchinsky, M. & Hahn, J. (1998) An alternative estimator for the censored quantile regression model. Econometrica 66, 627–651.CrossRefGoogle Scholar
Cai, Z. & Xiao, Z. (2012) Semiparametric quantile regression estimation in dynamic models with partially varying coefficients. Journal of Econometrics 167, 413–425.CrossRefGoogle Scholar
Chaudhuri, P. (1991a) Nonparametric estimates of regression quantiles and their local bahadur representation. Annals of Statistics 19, 760–777.CrossRefGoogle Scholar
Chaudhuri, P. (1991b) Global nonparametric estimation of conditional quantiles and their derivatives. Journal of Multivariate Analysis 39, 246–269.CrossRefGoogle Scholar
Chaudhuri, P., Doksum, K., & Samarov, A. (1997) On average derivative quantile regression. Annals of Statistics 25, 715–744.Google Scholar
Chen, S. & Khan, S. (2000) Estimating censored regression models in the presence of nonparametric multiplicative heteroscedasticity. Journal of Econometrics 98, 283–316.CrossRefGoogle Scholar
Chen, S. & Khan, S. (2001) Semiparametric estimation of a partially linear censored regression model. Econometric Theory 17, 567–590.CrossRefGoogle Scholar
Chen, S. & Khan, S. (2008) Semiparametric estimation of nonstationary censored panel data models with time varying factor loads. Econometric Theory 24, 1149–1173.Google Scholar
Christopeit, N. & Hoderlein, S. (2006) Local partitioned regression. Econometrica 74, 787–817.CrossRefGoogle Scholar
De Gooijer, J.G. & Zerom, D. (2003) On additive conditional quantiles with high-dimensional covariates. Journal of the American Statistical Association 98, 135–146.CrossRefGoogle Scholar
Deaton, A. & Muellbauer, J. (1980) An almost ideal demand system. American Economic Review 70, 312–326.Google Scholar
Efron, B. (1967) The two-sample problem with censored data. In Le Cam, L. & Neyman, J. (eds.), Proceedings of the Fifth Berkeley Symposium in Mathematical Statistics, IV, pp. 831–853. Prentice Hall.Google Scholar
Fan, J. & Gijbels, I. (1996) Local Polynomial Modelling and its Applications. Chapman and Hall.Google Scholar
Fan, J. & Zhang, W. (1999) Statistical estimation in varying coefficient models. The Annals of Statistics 27, 1491–1518.Google Scholar
Gonzalez-Manteiga, W. & Cadarso-Suarez, C. (1994) Asymptotic properties of a generalized Kaplan-Meier estimator with some applications. Journal of Nonparametric Statistics 4, 65–78.Google Scholar
Guerre, E. & Sabbah, C. (2012) Uniform bias study and bahadur representation for local polynomial estimators for the conditional quantile function. Econometric Theory 28, 87–129.CrossRefGoogle Scholar
Hardle, W. (1990) Applied Nonparametric Regression. Cambridge University Press.CrossRefGoogle Scholar
Hoderlein, S. & Mammen, E. (2007) Identification of marginal effects in nonseparable models without monotonicity. Econometrica 75, 1513–1518.Google Scholar
Honore, B., Khan, S., & Powell, J.L. (2002) Quantile regression under random censoring. Journal of Econometrics 109, 212–221.CrossRefGoogle Scholar
Horowitz, J.L. (1992) A smoothed maximum score estimator for the binary response model. Econometrica 60, 505–531.CrossRefGoogle Scholar
Horowitz, J.L. (1993) Semiparametric estimation of a work-trip mode choice model. Journal of Econometrics 58, 49–70.CrossRefGoogle Scholar
Horowitz, J.L. & Lee, S. (2002) Semiparametric methods in applied econometrics: Do the models fit the data? Statistical Modeling 2, 3–22.CrossRefGoogle Scholar
Horowitz, J.L. & Lee, S. (2005) Nonparametric estimation of an additive quantile regression model. Journal of the American Statistical Association 100, 1238–1249.CrossRefGoogle Scholar
Kim, M.O. (2007) Quantile regression with varying coefficients. The Annals of Statistics 35, 92–108.Google Scholar
Kong, E., Linton, O., & Xia, Y. (2013) Global bahadur representation for nonparametric censored regression quantiles and its application. Econometric Theory 29, 941–968.CrossRefGoogle Scholar
Lee, S. (2003) Efficient semiparametric estimation of partially linear quantile regression model. Econometric Theory 19, 1–31.Google Scholar
Lee, S. (2007) Endogeneity in quantile regression models: A control function approach. Journal of Econometrics 141, 1131–1158.CrossRefGoogle Scholar
Li, Q., Huang, C.J., Li, D., & Fu, T.T. (2002) Semiparametric smooth coefficient models. Journal of Business and Economic Statistics 20, 412–422.CrossRefGoogle Scholar
Peng, L. & Huang, Y. (2008) Survival analysis with quantile regression models. Journal of the American Statistical Association 103, 637–649.Google Scholar
Portnoy, S. (2003) Censored regression quantiles. Journal of the American Statistical Association 98, 1001–1012.Google Scholar
Powell, J.L. (1984) Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25, 303–325.Google Scholar
Powell, J.L. (1986) Censored regression quantiles. Journal of Econometrics 32, 143–155.CrossRefGoogle Scholar
Powell, J.L., Stock, J.H., & Stoker, T.M. (1989) Semiparametric estimation of index coefficients. Econometrica 57, 1404–1430.CrossRefGoogle Scholar
Robinson, P. (1988) Root-n-consistent semiparametric regression. Econometrica 56, 931–954.CrossRefGoogle Scholar
Sasaki, Y. (2015) What do quantile regressions identify for general structural functions. Econometric Theory 31, 1102–1116.CrossRefGoogle Scholar
Wang, H. & Wang, L. (2009) Locally weighted censored quantile regression. Journal of the American Statistical Association 104, 1117–1128.CrossRefGoogle Scholar
Wang, H.J., Zhu, Z., & Zhou, J. (2009) Quantile regression in partially linear varying coefficient models. Annals of Statistics 37, 3841–3866.CrossRefGoogle Scholar
Yu, K. & Lu, Z. (2004) Local linear additive quantile regression. Scandinavian Journal of Statistics 31, 333–346.CrossRefGoogle Scholar